# L-moments of the Generalized Pareto Distribution

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### Description

This function estimates the L-moments of the Generalized Pareto distribution given the parameters (ξ, α, and κ) from pargpa. The L-moments in terms of the parameters are

λ_1 = ξ + \frac{α}{κ+1} \mbox{,}

λ_2 = \frac{α}{(κ+2)(κ+1)} \mbox{,}

τ_3 = \frac{(1-κ)}{(κ+3)} \mbox{, and}

τ_4 = \frac{(1-κ)(2-κ)}{(κ+4)(κ+3)} \mbox{.}

### Usage

 1 lmomgpa(para) 

### Arguments

 para The parameters of the distribution.

### Value

An R list is returned.

 lambdas Vector of the L-moments. First element is λ_1, second element is λ_2, and so on. ratios Vector of the L-moment ratios. Second element is τ, third element is τ_3 and so on. trim Level of symmetrical trimming used in the computation, which is 0. leftrim Level of left-tail trimming used in the computation, which is NULL. rightrim Level of right-tail trimming used in the computation, which is NULL. source An attribute identifying the computational source of the L-moments: “lmomgpa”.

W.H. Asquith

### References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, pp. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

pargpa, cdfgpa, pdfgpa, quagpa
 1 2 3 lmr <- lmoms(c(123,34,4,654,37,78)) lmr lmomgpa(pargpa(lmr))